*
*Research Articles:

**Normalizer circuits and a Gottesman-Knill theorem
for infinite-dimensional systems** (pp0361-0422)

Juan Bermejo-Vega,
Cedric Yen-Yu Lin, Maarten Van den Nest

Normalizer circuits are generalized Clifford circuits that act on
arbitrary finite-dimensional systems $\mathcal{H}_{d_1}\otimes \cdots \otimes
\mathcal{H}_{d_n}$ with a standard basis labeled by the elements of a
finite Abelian group $G=\mathbb{Z}_{d_1}\times\cdots \times \mathbb{Z}_{d_n}$.
Normalizer gates implement operations associated with the group $G$ and
can be of three types: quantum Fourier transforms, group automorphism
gates and quadratic phase gates. In this work, we extend the normalizer
formalism \cite{VDNest_12_QFTs,BermejoVega_12_GKTheorem} to \emph{infinite
dimensions}, by allowing normalizer gates to act on systems of the form
$\mathcal{H}_\mathbb{Z}^{\otimes a}$: each factor $\mathcal{H}_\mathbb{Z}$
has a standard basis labeled by \emph{integers} $\mathbb{Z}$, and a
Fourier basis labeled by \emph{angles}, elements of the \emph{circle
group} $\mathbb{T}$. Normalizer circuits become hybrid quantum circuits
acting both on continuous- and discrete-variable systems. We show that
infinite-dimensional normalizer circuits can be efficiently simulated
classically with a generalized \textbf{\emph{stabilizer formalism}} for
Hilbert spaces associated with groups of the form $\mathbb{Z}^a\times \mathbb{T}^b
\times \mathbb{Z}_{d_1}\times\cdots\times \mathbb{Z}_{d_n}$. We develop
new techniques to track stabilizer-groups based on \emph{normal forms}
for group automorphisms and quadratic functions. We use our normal forms
to reduce the problem of simulating normalizer circuits to that of
finding general solutions of systems of mixed real-integer linear
equations \cite{BowmanBurget74_systems-Mixed-Integer_Linear_equations}
and exploit this fact to devise a robust simulation algorithm: the
latter remains efficient even in pathological cases where stabilizer
groups become \emph{infinite}, \emph{uncountable} and \emph{non-compact}.
The techniques developed in this paper might find applications in the
study of fault-tolerant quantum computation with superconducting qubits.

**Constructions of $q$-ary entanglement-assisted
quantum MDS codes with minimum distance greater than q+1** (pp0423-0434)

Jihao
Fan, Hanwu Chen, and Juan Xu

The entanglement-assisted stabilizer formalism provides a useful
framework for constructing quantum error-correcting codes (QECC), which
can transform arbitrary classical linear codes into
entanglement-assisted quantum error correcting codes (EAQECCs) by using
pre-shared entanglement between the sender and the receiver. In this
paper, we construct five classes of entanglement-assisted quantum MDS (EAQMDS)
codes based on classical MDS codes by exploiting one or more pre-shared
maximally entangled states. We show that these EAQMDS codes have much
larger minimum distance than the standard quantum MDS (QMDS) codes of
the same length, and three classes of these EAQMDS codes consume only
one pair of maximally entangled states.

**Multiparty quantum signature schemes** (pp0435-0464)

Juan Miguel
Arrazola, Petros Wallden, and Erika Andersson

Digital signatures are widely used in electronic communications to
secure important tasks such as financial transactions, software updates,
and legal contracts. The signature schemes that are in use today are
based on public-key cryptography and derive their security from
computational assumptions. However, it is possible to construct
unconditionally secure signature protocols. In particular, using quantum
communication, it is possible to construct signature schemes with
%information-theoretic security based on fundamental principles of
quantum mechanics. Several quantum signature protocols have been
proposed, but none of them has been explicitly generalised to more than
three participants, and their security goals have not been formally
defined. Here, we first extend the security definitions of Swanson and
Stinson \cite{swanson2011unconditionally} so that they can apply also to
the quantum case, and introduce a formal definition of transferability
based on different verification levels. We then prove several properties
that multiparty signature protocols with information-theoretic security
-- quantum or classical -- must satisfy in order to achieve their
security goals. We also express two existing quantum signature protocols
with three parties in the security framework we have introduced.
Finally, we generalize a quantum signature protocol given in
\cite{dunjko2014QDSQKD} to the multiparty case, proving its security
against forging, repudiation and non-transferability. Notably, this
protocol can be implemented using any point-to-point quantum key
distribution network and therefore is ready to be experimentally
demonstrated.

**Realizing an N-two-qubit quantum logic gate in a
cavity QED with nearest qubit--qubit interaction** (pp0465-0482)

Taoufik
Said, Abdelhaq Chouikh, Karima Essammouni, and Mohamed Bennai

We propose an effective way for realizing a three quantum logic gates (NTCP
gate, NTCP-NOT gate and NTQ-NOT gate) of one qubit simultaneously
controlling N target qubits based on the qubit-qubit interaction. We use
the superconducting qubits in a cavity QED driven by a strong microwave
field. In our scheme, the operation time of these gates is independent
of the number N of qubits involved in the gate operation. These gates
are insensitive to the initial state of the cavity QED and can be used
to produce an analogous CNOT gate simultaneously acting on N qubits. The
quantum phase gate can be realized in a time (nanosecond-scale) much
smaller than decoherence time and dephasing time (microsecond-scale) in
cavity QED. Numerical simulation under the influence of the gate
operations shows that the scheme could be achieved efficiently within
current state-of-the-art technology.

**Non-Markovian quantum trajectroy unravellings of
entanglement** (pp0483-0497)

Brittany Corn, Jun
Jing, and Ting Yu

The fully quantized model of double qubits coupled to a common bath is
solved using the quantum state diffusion (QSD) approach in the non-Markovian
regime. We have established the explicit time-local non-Markovian QSD
equations for the two-qubit dissipative and dephasing models. Diffusive
quantum trajectories are applied to the entanglement estimation of two-qubit
systems in a non-Markovian regime. In both cases, non-Markovian features
of entanglement evolution are revealed through quantum diffusive
unravellings in the system state space.

**Quantum interpretations of AWPP and APP** (pp0498-0514)

Tomoyuki Morimae
and Harumichi Nishimura

AWPP is a complexity class introduced by Fenner, Fortnow, Kurtz, and Li,
which is defined using GapP functions. Although it is an important class
as the best upperbound of BQP, its definition seems to be somehow
artificial, and therefore it would be better if we have some ``physical
interpretation" of AWPP. Here we provide a quantum physical
interpretation of AWPP: we show that AWPP is equal to the class of
problems efficiently solved by a quantum computer with the ability of
postselecting an event whose probability is close to an FP function.
This result is applied to also obtain a quantum physical interpretation
of APP. In addition, we consider a ``classical physical analogue" of
these results, and show that a restricted version of ${\rm BPP}_{\rm
path}$ contains ${\rm UP}\cap{\rm coUP}$ and is contained in WAPP.

**A localized quantum walk with a gap in
distribution **(pp0515-0529)

Takuya Machida

Quantum walks behave differently from what we expect and their
probability distributions have unique structures. They have
localization, singularities, a gap, and so on. Those features have been
discovered from the view point of mathematics and reported as limit
theorems. In this paper we focus on a time-dependent three-state quantum
walk on the line and demonstrate a limit distribution. Three coin states
at each position are iteratively updated by a coin-flip operator and a
position-shift operator. As the result of the evolution, we end up to
observe both localization and a gap in the limit distribution.

**Entanglement of simultaneous and non-simultaneous
accelerated qubit-qutrit systems** (pp0530-0542)

Nasser Metwally

In this contribution, we investigate the entanglement behavior of
a composite system consists of two different dimensional subsystems in
non-inertial frames. In particular, we consider a composite system of a
qubit(two-dimensional) subsystem and a qutrit (three-dimensional)
subsystem. The degree of entanglement is quantified for different cases,
where it is assumed that the two-subsystems are simultaneously or
non-simultaneously accelerated. The entanglement decays with the
increase of the acceleration of any subsystem. In general, the decay
rate of entanglement increases with higher dimension of the accelerated
subsystem. These results could be important in building an accelerated
quantum network consist of different dimensions nodes.